Order adaptive integration rule with equivalently weighted internal nodes

Abstract

Purpose

To develop order adaptive integration rule without limitation requiring that the number of equally spaced nodes must be a divisible numeral. Such integration technique could be of great practical value for different engineering applications where partition adaptability is impossible and use of standard high order integration techniques is unfeasible due to the fact that a significant number of nodes at the end of the sampling sequence must be deleted until the needed divisibility of the number of nodes is achieved.

Design/methodology/approach

Finite element approximation is used for the subdivision of the domain of integration and the development of order adaptive integration rule.

Findings

New integration rule is developed. It has a number of interesting features. Weights of the internal nodes are equivalent and equal to one. That makes the computational implementation of the integration rule very easy. Weights not equal to one are located only at the beginning and at the end of the sequence and are symmetric. For an m‐th order rule the number of weights not equal to one is 2m if m is odd.

Originality/value

For different engineering applications where the integration order can be controlled without changing the number of nodes, especially for real time applications where the number of discrete samples is unknown before the experiment.

Citation

Ragulskis, M. and Ragulskis, L. (2006), "Order adaptive integration rule with equivalently weighted internal nodes", Engineering Computations, Vol. 23 No. 4, pp. 368-381. https://doi.org/10.1108/02644400610661154